Are You Confusing Simplicity with Simple Mindedness?
…and why you should not
Goal: Discuss a strategy for solving problems
I want to go down memory lane a bit.
Many years ago I worked on my masters degree. What I found interesting about my masters was that it forced me to think more theoretically than my undergraduate degree ever did.
It seemed that almost every course required I do a proof to show that something was true or not. That seemed excessive to me but I pushed through it and eventually got good at doing proofs.
Why is that important?
The ability to solve a problem requires that we take the time to understand the assumptions that we come in with while trying to solve it. For example, you are trying to develop a budget for a project BUT the sponsor believes that the budget is $X millions. That assumption might prevent you from solving the problem.
While studying and doing these proofs I would often go back to the simplest case which I can definitely prove one way or another that it was true or not. I would then try to add on an assumption and prove a more difficult case. Add another assumption and solve that case. Eventually I would get to the general case with all of the assumptions.
This technique was never taught to me BUT while being irritated with a proof slowly worked into it. I was irritated enough, curious enough to keep working on it till success.
I recalled these experiences recently when I read an article about a Claude Shannon. Claude Shannon was a mathematical genius who dabbled in many fields and had a lot of different interests outside of research. He was brilliant and contributed to many areas of interest of information theory that we today take for granted.
BUT that is not the point of this story…
I read this passage from an article where one of his co-workers came to him with a problem. This is what Claude did:
“Gallagher recalled:
He looked at it, sort of puzzled, and said, “Well, do you really need this assumption?” And I said, “Well, I suppose we could look at the problem without that assumption.” And we went on for a while. And then he said, again, “Do you need this other assumption?”… And he kept doing this, about five or six times… At a certain point, I was getting upset, because I saw this neat research problem of mine had become almost trivial. But at a certain point, with all these pieces stripped out, we both saw how to solve it. And then we gradually put all these little assumptions back in, and then, suddenly, we saw the solution to the whole problem. And that was just the way he worked.”
The procedure he followed was identical to the one I used. Is it simple or simple minded?
I would argue that the procedure was a strategy that leads to solving more complex problems than just brute force. Start with things you know and can prove and then increase the difficulty.
My nineteen cents….(this is what I earned from Medium.com for Dec. 2020)
I gotta go…my future self alarm went off
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